text:
Why do most airliners have underwing engines, while business jets have rear-mounted engines?
Why have modern airliners converged on a configuration with two or occasionally four underwing engines, while modern business jets have converged on a configuration with two or occasionally three rear-mounted engines?
I am of course aware of the many past airliners with rear-mounted engines, with the DC-9 and MD-80 and later derivatives continuing into production until rather recently, but it still seems fair to say that the underwing configuration dominates modern airliner design.
Meanwhile business jets exclusively use the rear-engine design, unless one counts small airliners put into business service such as the Boeing Business Jet.  Does the underwing engine design simply not scale down well to something the size of a smaller business jet?
Here's a related question with good answers but still doesn't really answer my question-- How does the mounting location of a jet engine affect aircraft performance?
One key factor now occurring to me is that business jets are boarded with self-contained airstair doors/ steps so a fuselage sitting high off the ground would be problematic.  Airliners with long fuselages perhaps may need rather long landing gear to provide adequate ground clearance for rotation anyway-- although the DC-9 / MD-80 with its wing and landing gear far to the rear did sit rather low to the ground-- still in the airliner situation perhaps there simply is not as much benefit to having a low-sitting fuselage as there is in the business jet situation.
Of peripheral interest is this Wikipedia article on "airstairs", pointing out some cases where full-blown airliners are equipped with airstairs.  One of the more interesting lines is:

The most unusual airstair design was found on the Lockheed L-1011,
  which was a full-height airstair which was stored in a cargo
  compartment and allowed access from the right aft passenger door to
  the ground. This design was ultimately so large and heavy, and it took
  up valuable cargo space, that it was rarely used.

And the longer fuselage length of an airliner requires longer landing gear for adequate ground clearance for rotation anyway?  Maybe a key factor is that business jets need to be able to reach the ground with self-contained airstair doors/ steps?

Go ahead and post that as answer, It was your earlier comment (now deleted) that got me thinking along those lines--

You assume that all business jets are small. Boeing makes the BBJ from the 737 airframe. Airbus also has a corporate jet division that uses their airliner airframes.

A related question with good answers about why regional jets are moving toward a configuration with underwing engines -- https://aviation.stackexchange.com/questions/25636/why-are-modern-regional-jet-designs-shifting-towards-under-wing-engines?rq=1

Related-- "Regional and private jets, which often have fuselage-mounted engines, also tend to serve such smaller airports. These planes were designed with the engines mounted higher specifically to reduce the risk of ingesting FOD, thus allowing them to safely power back when needed." -- from https://aviation.stackexchange.com/questions/67219/how-and-why-does-the-atr-72-sometimes-use-reverse-thrust-to-push-back-from-its-p/67227#67227

Underwing engines have more advantages for larger planes, but there must be enough room underneath the wing to mount them.
This was tested by Boeing in the 1960s, when they designed the B737 and had two competing teams pre-design both configurations. The underwing config won. When Airbus designed the A320 two decades later, the underwing config won again with engines that were a good amount wider.

Image source.
Advantages of underwing mount:

Engines mounted in pods underneath the wing reduce the upward bending moment of lift creation, and therefore allows for lighter construction.
If the pods stick out forward of the wing, the backwards aerodynamic twisting moment is also reduced: lighter construction.
The engines can be easily reached for maintenance.
All of the fuselage can be used for useful load - tail mounted engines have structural reinforcements in the fuselage between the engines.

Advantages of fuselage mount:

The yawing moment of a single engine fail is smaller, allowing for a smaller vertical tail.
Fuselage can be lower to the ground and allow for low door sill height.
Landing gear can therefore be shorter.
Clean wing configuration.
Lower trim change due to thrust.
Less noise in most of the cabin.

In smaller planes, the wing bending & twisting moment is a relatively smaller constructive issue than in larger planes. And indeed, being closer to the ground allows for easier boarding via air stairs.

For a great example of the "must be enough room" issue, look at the Boeing 737.  Originally, it had underwing engines, but as the engines got bigger, they migrated forward in order to get enough ground clearance.

There is a rarely used 3rd option: over-wing engines. Same light construction as underwing, but with a low door sill height. AFAIK only the HondaJet and the unpopular '60s airliner VFW-614 use this configuration.

@Adam - coincidentally just this week we had this question showing the Beriev Be-200 with over-wing engines.

Also, rear fuselage-mounted engines tend to be a bit quieter for occupants, a non-trivial concern for private (jet) aviation customers

@costrom Indeed, have added.

Fuselage mount would also have the advantage of reduced ingestion of debris, wouldn't it.

Do fuselage mounts also have reduced yaw in a single-engine failure? That's the kind of advantage you hope not to use, but if you have to make other design changes to make a single-engine failure controllable, it could be a big advantage.

This also plays into the underlying problem of the 737 MAX. The newer and larger engines required moving them even further forward, which caused the plane to behave undesirably in certain cases and required the addition of a now infamous safety system.

Do fuselage mount imply "Less noise in most of the cabin."? The engines are closer and more directly attached to the cabin. Wouldn't that imply more noise? Obviously, a small jet will need smaller engines, and this per se implies less noise.

More noise at the back, less at the front.  It's a wash in the end.  In cruise, most of the noise is from the airflow.  Corporate aircraft use extensive and heavy sound insulation to control noise, which they can get away with because they aren't carrying many people.

@DanHulme yes there is somewhat less single engine yaw, but not as much as you'd think.  You still have to get on the rudder quick following a V1 cut or it rolls in its back, although the amount of rudder input is somewhat less.

@QuoraFeans Wing mount: most noise at the wing root, falling away with distance in both directions. Fuselage mount: same noise level at the aft fuselage (no passengers there because of the necessary structural reinforcements), falling away with forward distance (max. distance is twice that of a mid fuselage mount). The F100 is whisper quiet in the front cabin at cruise speed>

@JohnK The yawing moment is reduced, therefore the vertical tail is dimensioned smaller, therefore the aeroplane reactions are comparable.

@CraigMcQueen Yes, although debris ingestion has turned out to be not much of an issue. Statistically, that is.

Airliners are designed for loading from elevated passageways at airport terminals.  The terminal comes to the door you might say, so it doesn't matter so much how far off the ground it is.  And absent a terminal gate, you can always use an external staircase you move to the plane for the passengers/cattle to climb.
Business aircraft are designed to be boarded from the surface, traveling from limo to cabin in a luxurious, exclusive manner, usually using an airstair door.  You need a fuselage close to the surface for an airstair door to work.  This pretty much precludes underslung engines.
And if you did insist on trying to squeeze in a set of underslung engines under the wings, they'd be so close to the surface they'd ingest every sand grain and pebble.

+1 but I'll note that the boarding from the ground isn't only (and perhaps not even primarily) about luxury and exclusivity. One of the major advantages of travel by private / business jet is the ability to use small airports that are more numerous, not crowded and are more conveniently located than major airports with airline service. These smaller fields don't have jetways and often don't even have mobile passenger boarding stairs available. Hence airstairs.

@pericynthion: And even when landing at major airports, business jets (and other private aircraft) generally use facilities separate from passenger terminals.  For instance, at my local commercial airport, the passenger terminals are on the northwest side of the field, private facilities on the east and south sides.

Many of the Boeing 737s of Ryanair have built in stairs for the front door, so it's certainly possible to be self-sufficient in terms of getting on and off the plane even for planes with larger ground clearance.

Isn't that a chicken-egg phenomenon? We have elevated passageways because airliners are as high as they are. And we build airliners as high as they are so they fit the existing passageways. However, if it needed to be, passageways could be built at any height.

The passageways can go up and down quite a lot to accommodate various sizes of airliners. Main thing is airliners are boarded from controlled terminal facilities, business aircraft are boarded from the surface anywhere and everywhere and need airstair doors.  Airliners taller than CRJs (which are business jet derivatives), which include pretty much anything with underslung engines, are too tall for airstair doors to work.

Ground clearance
The single reason why an underwing design is unfeasible for smaller jets is just ground cleareance.
There are several reasons why smaller jets have lower ground clearance.
For once, higher ground clearance requires longer landing gears. These have to be stored in flight and take up valueable space and weigh more. On larger planes, the gear has to be sturdier anyways thus they need heavier and larger gears anyways since they have longer fuselages and more overall weight. In turn this reduces maximum range and payload of the aircraft and that is generally something you'd want to avoid.
Also a lot of smaller jets operate on smaller airports. Smaller airports have fewer gates with passenger bridges / stairs available (if they have any at all) and using a gate with one usally is attached to quite a hefty fee.
Considering that many business jets also have long durations of waiting on the ground, they are unlikely to ever be used at a gate with a passenger bridge anyways. Thus passengers have to be able to (dis-)embark easily without stairs / passenger bridges as they often will use GA parking spaces.
You can see that mostly on smaller jetliners too like the smaller Embraer or the McDonnell Douglas planes. The smaller designs tend to use rear mounted engines as they have a very low clearance below their wings.

The 737-200 had underwing engines.

@Koyovis no one said otherwise. A 737-200 is rather tall with a total height of 37ft compared to an MD80 with 29ft although their passenger capacity is quite similar.

"engine design simply [does] not scale down well" - on some airliners their enclosure is flat on the bottom.... Where you gonna put 'em, half way into the ground? +1


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FAR 91.215 (b)(3)(ii)-- transponders- significance of "Below the altitude of the ceiling of a Class B or C airspace area... or below 10,000' MSL..."
Clarification: this question was intended to address the situation before FAR 91.225 went into effect; please answer accordingly.  Feel free to also add additional content addressing the present situation now that FAR 91.225 has gone into effect.
Here are some of the airspaces where FAR 91.215 requires aircraft to have transponders--

(b) ...
(2) All aircraft. In all airspace within 30 nautical miles of an
airport listed in appendix D, section 1 of this part from the surface
upward to 10,000 feet MSL;
(3) Notwithstanding paragraph (b)(2) of this section, any aircraft
which was not originally certificated with an engine-driven electrical
system or which has not subsequently been certified with such a system
installed, balloon or glider may conduct operations in the airspace
within 30 nautical miles of an airport listed in appendix D, section 1
of this part provided such operations are conducted -
(i) Outside any Class A, Class B, or Class C airspace area; and
(ii) Below the altitude of the ceiling of a Class B or Class C
airspace area designated for an airport or 10,000 feet MSL, whichever
is lower;

Question 1: May an aircraft with no engine-driven electrical system and no transponder operate at 10,500' MSL in the airspace 10 miles west of South Valley Regional airport (U42) near Salt Lake City, where the overlying Class B shelf has a floor at 11,000', and a ceiling at 12,000' MSL? [(Link to sectional chart.)] 2
Note that KSLC is one of the airports listed in the Appendix referenced in FAR 91.215(b)(ii)-- this is a reference to the Mode C veil.
Question 2: May the same aircraft operate at 17,500' at the same location?
Question 3: (only applicable if the answers to (1) and (2) are both "yes")-- Does the "or below 10,000' MSL" clause of FAR 91.215(b)(3)(ii) have any actual practical significance of any kind?  What is an example of some airspace where an aircraft with no engine-driven electrical system and no transponder may not operate, but would be able to operate if the "or below 10,000' MSL" clause were absent from FAR 91.215(b)(3)(ii)?
Note that FAR 91.215(b)(3) is simply an exemption to 91.215(b)(2), which appears to only apply up to 10,000' MSL, so it appears at first glance that the answers to the questions ought to be "yes", "yes", and "no".  Is this really correct?
Question 4: What is the horizontal area affected by FAR 91.215(b)(3)(ii)?  Is an aircraft without a transponder flying below 10,000' MSL supposed to stay below the altitude of the ceiling of any Class B or Class C airspace designated for an airport that happens to be within the 30-nm Mode C veil, even if the aircraft is horizontally distant from any portion of that airspace?  If so, what if there is more than one than one such airport, and they have different ceilings?
Question 5: Does FAR 91.215(b)(3)(ii) have any practical significance of any kind at all?  Would it ever affect where any aircraft may operate?

Aren't the jets allowed to really ratchet up their speed above 10,000? Like the 250 knot limitation goes away? I don't think the FAA/ATC wants some small plane puttering along that they don't know about and having it be run over by something fast.

These links don't consistently display well.  Have I used a format that is no longer supported?

Related: https://aviation.stackexchange.com/questions/74857/does-the-faa-construe-far-91-225-to-prohibit-aircraft-w-o-electrical-systems-w-o

"Significance of" might better read "meaning of".  Re question 3: the clause is actually " "or (below) 10,000' MSL, whichever is lower".   This question really needs actual images from the sectional charts.  glider and balloon tags could be added, as they rarely have transponders.

The answers to Questions 1,2, and 3 are "yes", "yes", and "no".  Neither FAR 91.215(b)(2) nor FAR 91.215(b)(4) have any effect above 10,000' MSL.
The "or below 10,000' MSL" clause in 91.215(b)(3)(ii) has no effect on anything at all and does not prevent an aircraft not certificated with an engine-driven electrical system from operating above Class B or Class C airspace as long as it is above 10,000' MSL.
The answer to question 4 is "no, an aircraft that is completely outside of the lateral boundaries of a given Class B or Class C airspace cannot be violating FAR 91.215(b)(3) in relation to that airspace, regardless of altitude."
All of this is clarified in this 2006 interpretation from the FAA Office of the Chief Counsel:

Section 91.215 does not prohibit gliders or sailplanes not equipped
with transponders from operating above 10,000 feet MSL and thus above
the ceiling of and outside Class B airspace.

and

"The practical effect of paragraph (b)(3) with respect to your
question is that it allows non-equipped aircraft to enter the
30-nautical mile circles surrounding Appendix D, Section 1 airports
between the surface and 10,000' MSL and to operate beneath the floors
of the associated Class B airspace..."

and

In the context of your question, subparagraph (b)(4) would prohibit an
unequipped glider or sailplane from operating in the ‘wedge’ of
airspace that may exist directly above Class B or Class C airspace and
below 10,000 feet MSL. If the ceiling of the Class B or Class C
airspace is at 10,000 feet MSL, then subparagraph (b)(4) is rendered
moot.

The answer to question 5 therefore appears to be "regardless of the actual wording, FAR 91.215(b)(3)(ii) should simply be interpreted as an indication that 91.215(b)(3) does not give relief from 91.215(b)(4), which requires a transponder for flying "above the ceiling and within the lateral boundaries of a Class B or Class C airspace area designated for an airport upward to 10,000 feet MSL".  Meaning that even aircraft not certified with engine-driven electrical systems are not exempt from the transponder requirement in the airspace directly above Class B and C ceilings, up to 10,000' MSL.  In other words, there is an unstated implication that 91.215(b)(3)(ii) does not apply to any airspace that lies beyond the lateral boundaries of Class B or Class C airspace.  This could have been more clearly accomplished by other means, for example by replacing the text of 91.215(b)(3)(ii) with the simple phrase "clear of the airspace described in 91.215(b)(4)".

However...

It's important to note that the fundamental reason that FAR 91.215(b)(3)(ii) has no effect on anything that happens above 10,000' MSL is that 91.215(b)(3)(ii) is spelling out the terms under which certain aircraft can operate contrary to 91.215(b)(2), and 91.215(b)(2) explicitly has no effect on any airspace above 10,000' MSL.

As a thought experiment, we can ask ourselves "If 91.225 had never been introduced, but 91.215(b)(2) were modified tomorrow to extend up to 15,000' MSL, then is there anything either in the literal language of 91.215(b)(3)(ii), or in the logic used in the 2006 interpretation referenced above, that would allow aircraft (not certificated with engine-driven electrical systems) lacking transponders to fly in any of the airspace below 15,000' directly above the ceiling of Class B or Class C airspace that lies within a Mode C veil?"  The answer appears to be "No, all the airspace between the Class B or Class C ceiling and 15,000' MSL would be off-limits to such an aircraft in that case."  The point being that since 91.215(b)(2) doesn't apply above 10,000' MSL anyway, the 2006 interpretation shouldn't be read to construe that language used in 91.215(b)(3)(ii) inherently could never affect airspace above 10,000' MSL, and there's nothing in the actual language of 91.215(b)(3)(ii) that indicates that either.

In fact, by similar logic, the 2006 interpretation doesn't even unambiguously indicate that the "or (below) 10,000' MSL, whichever is lower" portion of the language of 91.215(b)(3)(ii) inherently should never be construed to apply to any airspace that does not directly overlie a Class B or Class C ceiling.  After all, if the "or (below) 10,000' MSL, whichever is lower" portion of the language used in 91.215(b)(3)(ii) were construed to apply to all airspace, even airspace outside the lateral boundaries of any nearby Class B or Class C airspace, this would simply mean that pilots who are using 91.215(b)(3)(ii) as a way to operate contrary to 91.215(b)(2) would have to stay below 10,000' MSL, and 91.215(b)(2) doesn't apply above 10,000' MSL anyway, so above that altitude the point is moot.

All this has unfortunate consequences for the clarity, or lack thereof, of the newer FAR 91.225, the ADS-B-out requirement, which unfortunately has incorporated language identical to that used in 91.215(b)(3)(ii).

The specific issue is FAR 91.225(d)(4), which explicitly does apply to airspace above 10,000' MSL. It's unclear exactly how aircraft (not certificated with engine-driven electrical systems) operating above 10,000'MSL and 2,500' AGL without ADS-B-out can be construed to be in compliance with FAR 91.225(e)(2) in any of this airspace, and particularly in the portions that lie directly above the ceilings of Class B or Class C airspace.

For more, see the related ASE question Does the FAA construe FAR 91.225 to prohibit aircraft w/o electrical systems w/o ADS-B-out from flying above 10,000' MSL unless below 2500' AGL?

Related: https://aviation.stackexchange.com/questions/74857/does-the-faa-construe-far-91-225-to-prohibit-aircraft-w-o-electrical-systems-w-o

(sorry, saw something else that had to fix, that's all for today)

RE just before the "However" section-- the statement "In other words, there is an unstated implication that 91.215(b)(3)(ii) does not apply..."-- could perhaps be better stated "...there is an unstated implication that 91.215(b)(3)(ii) does not restrict any a/c from flying in any airspace that lies beyond the lateral boundaries of Class B or Class C airspace, at least if that airspace lies below 10,000' MSL.

(ctd) ... The horizontal extent of the area that would be affected by the "or (below) 10,000 MSL, whichever is lower" portion of the language of 91.215(b)(3)(ii) is arguably a little less clear, except for the fact all of the airspace affected by 91.215(b)(2) lies below 10,000' MSL, so anything above that is a moot point anyway and can never be affected by 91.215(b)(3)(ii).  Also: bullet point 3: replace "portion of the language" with "phrase in the language."

Or "should only be understood to restrict a/c from flying in airspace that lies directly above... "

Point 3-- delete "nearby"

How do you interpret "...or 10,000 feet MSL, whichever is lower;" to give you a yes answer to # 1 & 2?  10K is lower than both 10.5K and 17.5K in the examples given, and should be controlling for each.  What am I missing?

@MichaelHall -- in FAR 91.215, (b)(3) describes how some aircraft may operate at variance with (b)(2).  How then could (b)(3) have any bearing on any airspace outside the scope of (b)(2)?  And all airspace above 10,000' MSL is outside the scope of (b)(2).

@MichaelHall-- the FAA's wording is awkward.  It would have been much clearer if they had said "(b)(3) Notwithstanding paragraph (b)(2) of this section, any aircraft which was not originally certificated with an engine-driven electrical system or which has not subsequently been certified with such a system installed, balloon or glider may conduct operations in the airspace described in (b)(2) provided such operations are conducted-"

It's a set theory problem.  (b)(2) applies to airspace that lies in the intersection of two sets, one set being the airspace below 10,000' MSL and one set being the airspace within 30 nautical mile...  (b)(3) is phrased as an exception to (b)(2) for certain aircraft, and so it can't apply to any set of airspace that is larger than the set of all airspace which is governed by (b)(2).

If (b)(3) was meant as a self-contained regulation rather than as an exception to another regulation,  it would be written using phrases like "must", "must not", or "may not", rather than simply saying how certain aircraft "may" operate.  Unless the FAA is operating under a philosophy that "any action not specifically permitted, is prohibited"!

It's admittedly a bit of a linguistic "train wreck" that may not have a clear solution from a strictly logical point of view.  I just don't think it makes sense to construe a regulation that is phrased as explaining how some aircraft may operate in contrary to another regulation, as affecting additional airspace that isn't addressed in the other regulation, e.g. the airspace above 10,000' MSL within 30 nm of... (etc etc).  At the end of the day, fortunately, we have the FAA interpretation cited in the answer to fall back on.

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text:
Are loops or rolls allowed in the "utility" category in any US-certified airplane or glider?
In actual practice, is there any US-certified airplane or glider where the approved flight manual, or cockpit placards, indicate that loops, rolls, or any other similarly aerobatic maneuvers other than "spins (if approved for plane), lazy eights, chandelles, and steep turns, or similar maneuvers, in which the angle of bank is more than 60 degrees but not more than 90 degrees" are allowed when the aircraft is operated in the "utility" category?
Also, in theory, would it ever be permissible for this situation to occur for a US-certified airplane or glider, if the manufacturer proved that the aircraft was safe for the maneuver in question?  Perhaps in conjunction with additional restrictions on weight or CG location?
See this closely-related question that notes that this IS the case for some airplanes and gliders certified in other countries: In the US, would it ever be legal to fly a loop in any airplane or glider that was operating in the "utility" rather than "acrobatic" category?
The current question is only asking about US-certified airplanes or gliders.

Several answers to this very  peripherally-related question about civilian aerobatics in the T-38 suggests that at a minimum, the FAA would want to see flight tests demonstrating said maneuver before allowing such a thing, and more generally tends to suggest the answer is likely "no" -- https://aviation.stackexchange.com/questions/21182/what-would-prohibit-a-t-38-talon-from-being-certified-in-the-acrobatic-category?rq=1

The main difference between Utility and Normal category in FAR 23 is spins and the limitation of bank angles in maneuvers.  Normal category is banks up to 60 deg and no spins.  Utility allows spins if certified for them, and banks up to 90 degrees.

Limited   acrobatic   operation includes: (1)  Spins  (if  approved  for  the  par-ticular type of airplane); and (2) Lazy eights, chandelles, and steep turns,  or  similar  maneuvers,  in  which  the  angle  of  bank  is  more  than  60  de-grees but not more than 90 degrees.

I would imagine that a Hammerhead, being a chandelle taken to an extreme, would be allowable since done properly the wings don't go beyond 90 deg,  but loops and rolls are definitely out in Utility Category.

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text:
Would all these three things have the exact same effect on the flight duration of a glider?
Consider a glider trimmed to fly at some given angle-of-attack, gliding in smooth air (no thermal convection, ridge lift, wave lift, etc.).  If air density is somehow kept exactly constant in all cases, and the glider is launched from the same initial altitude relative to the ground in all cases, would the flight duration be the same in all three cases?  (A yes/no question.)

Extra weight has been added to the glider, exactly at the CG, doubling the glider's weight.
We've increased the value of the gravitational constant from 9.8 m/s/s to a higher value (twice as high).
We've caused the earth (and atmosphere) to steadily accelerate straight “up”, at 9.8 m/s/s, thus creating an apparent increase in the gravitational constant (to an apparent value double the actual value).  (Acceleration starts well before the glider is launched, not mid-flight.  Glider is also accelerating along with everything else at instant of launch, i.e. the atmosphere isn't rushing up past the glider at the instant of launch.  For example the glider could launch by rolling off a ramp mounted on a high tower connected to the ground.)

(Edit: to make this more clear, imagine that a giant rocket engine attached to the other side of the earth is causing this acceleration.  The earth itself is the only thing that is being directly acted on by the accelerating force; the atmosphere and glider each experience the results of this acceleration in a less direct manner.)
Also, if “yes”, then a second question — launched in equilibrium (exactly at its steady-state trim speed for the existing conditions) from a given height, would the glider stay up for a longer duration or a shorter duration after we've made one of these changes?
The intent of the question is to compare the steady-state in-flight dynamics, not some difference  relating to some possible slight variation in the initial kinetic energy imparted at the instant of launch, etc.  In each case, the glider is understood to be launched at its steady-state trim speed in relation to the existing conditions.

Related: https://aviation.stackexchange.com/questions/66892/what-makes-airplane-fly-does-bernoulli-principle-still-reliable , https://wiki.tfes.org/Evidence_for_Universal_Acceleration ,

Also related: https://aviation.stackexchange.com/questions/606/why-would-a-glider-have-water-ballast-if-it-is-trying-to-stay-aloft-without-an

And just for more laughs-- https://wiki.tfes.org/Flat_Earth_-_Frequently_Asked_Questions

Natl Geo on flat earth: https://www.youtube.com/watch?v=06bvdFK3vVU

Scenarios 2 and 3 would be almost exactly the same. Scenario 1 would be very different. However, the glider would be able to stay up for almost exactly the same amount of time in all three scenarios.
The basic summary of what would happen: In scenario 1, both the weight and the mass would be doubled. In scenarios 2 and 3, the weight would be doubled but the mass would remain the same.
The simplest way to distinguish scenario 1 from the others is to pitch into a vertical climb (or a vertical dive). In scenario 1, the glider will accelerate downwards at $1\ g$, but in scenarios 2 and 3, it'll accelerate downwards at $2\ g$.
Scenarios 2 and 3, on the other hand, are almost completely identical. Specifically:
Scenario 2 simply adds more gravity. Pretty straightforward.
Scenario 3 consists of having the ground accelerate "up" at $1\ g$. We can look at this scenario in a frame of reference where the ground remains stationary. In this frame of reference, everything is just like the real world, except that everything is now experiencing an inertial force equal to $1\ g$ straight down.
How does an inertial force work? Inertial forces feel just like gravity. In fact, the only differences between the extra forces in the two scenarios are:

In scenario 2, the direction of the extra force changes as you move horizontally, because the direction of "down" changes as you move. In scenario 3, the extra force is in the same direction everywhere: namely, the direction opposite the direction of acceleration.
In scenario 2, the extra force gets weaker as you get farther away from the earth. In scenario 3, the extra force is equally strong everywhere.

Both of these differences are probably too small to measure.
Now, finally, I said that the glider will be able to stay up for the same amount of time in all three scenarios. This is because, although the mass of the glider differs between the three scenarios, its weight is the same in all three scenarios. And if the glider is flying at a constant speed in a straight line, weight is the only quantity that matters; mass is now irrelevant, because the glider is not accelerating (in the frame of reference where the earth is stationary).

Hope I didn't change the question on you before you answered; I suspect we were both typing at the same time.

For example the original question said "flight characteristics" which might include some up and down maneuvers but the intent was still to look at the steady-state glide only; the final version is more consistent with that.  Good points about the mass difference.  Can roll back if needed to something that still references "flight characteristics" or you could mod your answer to still reference the difference in flight characteristics as a point of interest.

Actually I feel your answer is still perfectly fine given the existing state of the question as you explicitly said "Now, finally, I said that the glider will be able to stay up for the same amount of time in all three scenarios. "

Looks like I just forgot which scenario was 2 and which was 3; I'll fix my answer now.

"The simplest way to distinguish scenario 1 from the others is to pitch into a vertical climb (or a vertical dive). In scenario 1, the glider will accelerate downwards at 1 g1 g, but in scenarios 2 and 3, it'll accelerate downwards at 2 g2 g." -- I'm not actually quite sure this is true.  I think starting in steady-state flight and then pitching straight down, all three will hit the ground at the same time.  Although no longer strictly related to the yes/no question asked, I'd be interested to know if you change your mind on this part after some further reflection.

It's not completely obvious to me, really.

Hmm, looks like I forgot to specify "flat earth" or "round earth" :)

@quietflyer "I think starting in steady-state flight and then pitching straight down, all three will hit the ground at the same time." Well, I'm not quite sure why you think that. The equation for acceleration is $a = F/m$; in scenarios 2 and 3, the gliders are experiencing twice as much force as originally, but they still have their original mass, so they'll accelerate twice as fast. The steady-state dive speed will be the same in all three scenarios, though.

Agreed , thanks.

If you wish you might want to address second-last-paragraph which was part of the editing that may have occurred while we were both typing, Anyway great answer.

Incorrect answer

@Jimmy Would you like to be more specific about what part of it is incorrect?

@TannerSwett Upon clarification that the OP is considering an isolated box scenario, I agree with your assessment.


text:
With power off, is it possible to maintain constant altitude for some period of time, until the stall speed is reached?
With power off, is it possible to maintain constant altitude for some period of time, until the 1-G stall speed is reached, i.e. until the stall angle-of-attack is reached?
Implicit in the question is the assumption that the initial airspeed is above the 1-G stall speed.

Why ask such a question?  The answer seems completely obvious, but discussion under this related question https://aviation.stackexchange.com/questions/66366/what-is-the-regular-stall-speed-of-f-16-flying-in-a-straight-and-level-path?noredirect=1#comment173477_66366 suggests we may see some "interesting" answers posted.

@AEhere -- modified.  Anything else that you need to know?

No, I just wanted you to avoid needless discussion by eliminating the trivial case.

Yes, assuming your are flying level with the engine running and then you turn the engine off, the following will happen:

Without power from the engine, the drag will cause the airspeed to decrease.
Lower airspeed at the same angle of attack implies less lift. Since you want to maintain altitude, lift needs to stay the same (your weight has not changed). Thus, you have to increase pitch.
Eventually, you will reach the critical angle of attack and flow separation will occur, i.e. you stall. The airspeed at which this happens is called the 1-G stall speed, although one can stall any speed.

Yes, this is how you practice stall recovery.

reduce power to idle
continue pulling back (that is to say, increase angle of attack) to maintain altitude until stall warning sounds
recover by lowering the nose and then re-applying power

Btw it's not how I usually practice stalls-- why worry about holding altitude exactly constant?  Exactly what is gained by that?  But it is indeed a common way to practice stalls.

I didnt say "exactly constant". I said "maintain". If you constantly lose altitude while practising stalls it just prolongs the amount of time you're maintaining slow flight, and the possibility of an unexpected wing drop.

... plus if you know how to practice a stall, then you know the answer to the question.

I don't mind the downvote for asking an obvious question, but if you are curious about the context and motivation, read the comments under https://aviation.stackexchange.com/questions/66366/what-is-the-regular-stall-speed-of-f-16-flying-in-a-straight-and-level-path?noredirect=1#comment173477_66366 .


text:
What is the formula for the bank angle required for a turn in line-abreast formation?
Imagine we have a line-abreast formation of aircraft, with differing airspeeds, turning around a central pivot point, like points on the radius of a phonograph record, with an equal amount time per 360 degrees of turn for each aircraft.  What is the formula for the bank angle required of each aircraft, in terms of the variables 1) turn radius and 2) time period per 360 degrees of turn?
Note that essentially the same situation applies when a slow-flying glider-- maybe even a hang glider-- and a faster, heavier glider are thermalling together and trying to stay exactly opposite each other.  Again the turn rate must be the same for each, but the turn radius is not, and the required bank angle for each might be different.  Clearly, the difference in turn radius is much more significant in this case, than in the case of high-speed aircraft turning in tight formation.

I can roll back the edit if it is felt that it invalidates existing answers; that was not my intent and my feeling is that it does not.  Note also the original specification of "differing airspeeds" implied that I was not interested only in the case of a tight formation of very-high-speed airspeed aircraft doing a turn of huge radius.

Your change invalidates Michael's answer.

Well, I guess then I or someone will roll it back at some point.

Turning Rate
All planes flying a turn in line-abreast formation are turning at the same rate $\omega$.
A standard turn is commonly defined as $\omega_1 = 3°\frac{1}{\mathrm{s}}$.
Full Circle Time Period
If planes are turning at the same rate, the time period to complete a complete circle will be the same as well.
Time period: $$ T(\omega) = \frac{360°}{\omega}$$
The time period to complete a circle at this standard turn rate is $T_1 = \frac{360°}{3°}\mathrm{s} = 120\,\mathrm{s}$.
Air Speed
Since the outer planes have to travel a longer distance to complete their larger circle in the same perios, the outer planes have to fly at a higher airspeed then the inner planes.
Air speed: $$ v = \omega r$$
Bank angle
Turn rate: $$\omega = \frac{v}{r}$$
Banking angle:  $$\tan{\theta} = \frac{v^2}{rg} = \frac{\omega^2 r}{g}$$
Gravitational constant: $$ g = 9.81 \frac{\mathrm{m}}{\mathrm{s^2}}$$
That gives the banking angle as a function of turning radius: $$\theta(r) = \arctan{\frac{\omega^2 r}{g}}$$
See the purple curve in the graph below for the bank angle in a standard rate turn (3°/s):

This curve seems to imply that one can fly a standard turn (or any other given turn rate) at any radius from 0 to infinity. Therefore I added two more curves to indicate the physical limits:

air speed (green) must be in the operating range of the plane
g load (blue) must not exceed the maximum acceptable for plane and occupants. (The correct scale for the g load is the purple scale on the left divided by 10)

And finally, the same plot but for a double rate turn (6°/s):

Practical Relevance
Typical turn radii are in the order of 1000s of meters. Typical distance (wing span) of planes in a tight formation is in the order of a few 10 meters, that is a few percent of the turn radius.
If you compare the banking angles for two planes flying in tight line-abreast formation, the banking angle difference will have a similar relative difference, that is a few percent, or a fraction of 1° in absolute terms.
[I will calculate and insert an example here, when I have the time.]
For the practical purpose of actual formation flying, pilots will give the arcus tangens a break, and fly seemingly identical banking angles.

I am still trying to figure out whether our answers are identical-

It looks like you started out talking about turn rate in terms of degrees per time but than you switched to radians per time-- is that correct?  That's what was throwing me for a bit.  Yes I see that they are the same now.

suggestion for next time: put the legend in a corner of the image with no lines (in this case, either top left or bottom right) took me a while to understand that "g load" in the first picture.

Hmm-- I was thinking I was the one who didn't need to decide, P (period) was time for one circle. w is a rate and so needs angular units as well as time units.  I think the answer could use some clarification when you make the switch, but anyway it is a good answer and I see the math is the same as mine.

For all practical purposes, to maintain a line abreast formation the angle of bank and rate of turn will need to be constant, while airspeed will vary with aircraft on the outside of the turn needing to speed up.

Why the downvotes?  How many voting have actually trained and flown in a line abreast formation?  I speak from years of real world practical military pilot experience:  You have to match the lead aircraft's AOB whether line abreast or in echelon.  If you bank differently than your flight lead you will either turn into him, or diverge away.  That is an observable, repeatable fact that doesn't rely on any mathematical equation!

I am not a mathematician, I just fly airplanes.  I understand equations, but I don't create them in an attempt to demonstrate knowledge of something I have no experience actually doing.

@quietflyer If they fly different radii, they might end up with same bank angle due different speeds. If they fly same radius, they can’t stay opposite each other at different speeds. The example is not obvious to me!?

For faster aircraft the line "abreast" turn could be easily done with change in speed, as speed squared is proportional to radius. Just as long as the inner does not stall and the outer does not exceed Vne.  Another turning technique from yesteryear is to have the inside plane climb and go outside and the outside dive and go inside.  But that wouldn't be abreast.

As @quiet flyer has strong experience in gliders, the question seems to focus on "how do we stay in a thermal with limited radius if my flying speed is different than yours?"
As flight is 3 dimensional, there is a vertical option.
But for the sake of discussion (maybe for a photo shoot) they both need to hold the same
altitude and remain at opposite points of a circle.
In order to have the same rate of turn, the faster must have the outside track.  Since radius is proportional to the SQUARE of speed, the radius of a 60 mph glider will be more than double that of a 40 mph glider if they use the same bank angle.  Note the difference in radii means they do not have to stay opposite in the thermal!
According to the radius of turn formula R = V^2/11.26×tanbankangle one can decrease their turn radius by increasing bank angle.  The rub is that higher AOA or greater speed is needed at a higher bank angle to generate adequate vertical lift.
Decreasing turn radius by increasing bank angle and AOA will allow one to "catch up" with the other.  ROT=1091xtanbankangle/airspeed. Decreasing bank angle and AOA has opposite effect.
But notice radii formula has V^2 and ROT formula does not square speed.  The distance travelled in the different size circles (pi x D) is linear with speed for equal rate of turn.
Radius at constant bank angle is dependent on the SQUARE of speed, whereas ROT is linear with speed. What to do?

Outside plane increases bank angle and AOA to increase ROT.
Inside plane decreases bank angle and AOA to decrease ROT.

As we can see what actually happens is highly dependent on the flight envelope of each aircraft. The inside one is safer by lowering bank angle and AOA.  But if speed difference is too much, they cannot remain in circular "formation".

For keeping a good visual lookout it is desirable that two aircraft thermalling together stay basically opposite each other.  Taking the basic case where one has a significantly faster stall speed than the other and both desire to circle just above stall speed (or more precisely just below stall angle-of-attack)  to maximize climb rate, in practice the faster one will need more bank angle to stay opposite the other one, and the faster one will also fly at a greater radius.  I really didn't mean to throw in such a wrench in the gears by not mentioning the glider situation sooner!

It all seems a variant of the original question to me, but I can see why all might not agree.

In actual practice while thermalling you decrease your bank angle if you wish to fall back relative to the other glider and increase it if you wish to move forward.

"they both need to hold the same altitude and remain at opposite points of a circle." That would put them at equal radii, though, which is at odds with the following paragraph. I think. The whole "they do not have to stay opposite in thermal", besides being much improved without caps, is a bit unclear.

Please see edits to answer.

I think there is no limit to the difference in speeds that can be accommodated and have them still stay opposite.  One just would end up having a much greater turn radius.  I suppose it's the case that there's a certain lower limit to the bank angle that faster aircraft can choose and still be within the radius of the thermal at all, which perhaps means that sometimes in practice the slower aircraft must accommodate its turn rate to the faster one and not vice versa.

This is a good one.  If I increase speed 40%, my radius doubles, there for my speed must go to 200% to stay in formation.  At some point the inner plane is too slow to fly and the outer plane hits its G limit.  But for @Michael Hall "practical purposes", as long as the difference in radius and speed can be covered with a little more bank, "abreast" works fine.  But for 2 gliders trying to hold Vbg, you run out of bank angle if speed difference is too great, especially trying to stay in the thermal "cylinder".  Will try for math formula.

It seems to me that whatever bank angle the faster glider is using, some shallower bank angle will be suitable to allow the slower glider to hold position across the circle.  I don't see any real problem here, unless the faster glider cannot stay in the thermal at ANY bank angle below the acceptable G-load, in which case the presence of the slower glider really isn't the problem at all.

Using the formulae $F_c = m * \frac{v^2}{r}$ and bank = arctan (Fc / (mg)), we can derive the formula bank = arctan (4*pi^2 *r / (P^2 * g)), where Fc is centripetal force, g is the gravitational constant, and P is the period or the time for one complete turn. The aircraft flying at a larger turn radius must use a larger bank angle than the aircraft flying at a smaller turn radius.
Note that mass or weight does not appear as a  variable in the final equations.
Note that v represents True airspeed-- the relationship between bank angle and turn rate or turn period (time per turn) or turn radius is not independent of density altitude.
Read on only if you want to see the math in more detail:
v=d/t = 2pir/P
bank angle= arctan(horizontal force/ vertical force)
=arctan (centripetal force/weight)
=arctan ((mv^2/r)/(mg))
=arctan ((v^2)/(rmg))
=arctan ((2pir/P)^2/(rg))
=arctan (4pi^2r/(g(P^2)))
Related link--
A link to an aviation website giving a rule of thumb for bank angle for a standard rate turn-- the rule of thumb is that the bank angle in degrees should be roughly .15 * (True airspeed in knots).

See also related question https://aviation.stackexchange.com/questions/65617/does-pumping-fuel-to-each-wingtip-affect-roll-trim-in-a-stabilized-turn

Yes, if...  What variable defines the speed?

Not sure I understand the last question.  It is easy to see the relationship between v (speed), r (radius), and P (period, or time for one circle.)

Lots of downvotes-- should I modify to show more of the math?

Please use mathias, there's a tutorial on the site

One situation where the difference in required bank angle may actually be noticeable is when fast and slow gliders are circling together in a thermal and trying to stay directly opposite each other, i.e. trying to fly at identical tun rates.  I've certainly felt that I've observed a difference in the required bank angle.

@Koyovis it's mathJax (guess it was an autocorrect-induced typo)

@Koyovis - got it, will look at that a bit later

This answer could be made more interesting by also providing the final formula in terms of v (true airspeed), and checking the answer against the rule-of-thumb in the link at the end, though that's not what the original question asked for.


text:
In the US, are inside loops permitted while flying a US- registered DG-1000S sailplane in the "utility" category?
Are inside loops are permitted while flying a US-registered DG-1000S sailplane in the US in the utility category?
FAR 91.1 seems highly relevant:

§91.9   Civil aircraft flight manual, marking, and placard
  requirements.
(a) Except as provided in paragraph (d) of this section, no person may
  operate a civil aircraft without complying with the operating
  limitations specified in the approved Airplane or Rotorcraft Flight
  Manual, markings, and placards, or as otherwise prescribed by the
  certificating authority of the country of registry.

More information: the English version of the factory-produced flight manual for the German-made DG-1000S glider (may be downloaded here) states the following--

2.6 Approved manoeuvres Category „Utility“: The glider is certified for normal gliding in the "Utility" category. Simple aerobatics are
  approved but only without waterballast and with the weight of the rear
  pilot compensated by ballast in the ballast box in the fin see section
  6.8.7.
The following aerobatic manoeuvres are approved with all spans:
Spins
Chandelle
Inside loop
Turn
Lazy Eight
Recommended entry speeds see section 4.5.8.1.

The manual then goes on to describe additional maneuvers allowed when flown at a lower weight limit, in the "aerobatic" category:

In addition to the manoeuvres in category „Utility“ the following manoeuvres are approved:
Inverted flight
half flick roll from normal to inverted flight with half loop
half loop and half roll
half flick roll from inverted to normal flight
half roll and half loop
slow roll

Before answering, you may wish to  consider the significance of the last quoted phrase in FAR 91.9, "or as otherwise prescribed by the certificating authority of the country of registry".  A "yes" answer to the basic question implies that this phrase in FAR 91.9 does not somehow prohibit looping a US-registered example of this glider in the US.

This question is a pared-down version of a broader multi-part question that is receiving few answers: https://aviation.stackexchange.com/questions/66531/in-the-us-would-it-ever-be-legal-to-fly-a-loop-in-any-airplane-or-glider-that-w

Stuff you quoted in your question seems to provide the answer you're after:

2.6 Approved manoeuvres Category „Utility“: The glider is certified for normal gliding in the "Utility" category. Simple aerobatics are approved but only without waterballast and with the weight of the rear pilot compensated by ballast in the ballast box in the fin see section 6.8.7.
The following aerobatic manoeuvres are approved with all spans:
...
Inside loop

I think you are right- just wondered whether any problem was caused by that last quoted phrase in FAR 91.9, "or as otherwise prescribed by the certificating authority of the country of registry".

I'm assuming that the "certificating authority of the country of registry" would mean the FAA- do they even officially approve the flight manuals, placards, etc of an aircraft certified in another country?

I'm not familiar with other countries, I've only flown in the US and the Bahamas. Might fly in Canada sometime, need to apply for international use radio license, any maybe do something for 121.5 MHz ELT as I have updated to 406 MHz GPS ELT.


text:
In the US, how does the distinction between E2 and E3/E4 airspace affect pilots?
In the US, practically speaking, how does the distinction between the E2 and E3/E4 subtypes of Class E airspace affect pilots?

This question + self-answer was posted in response to a comment/ request from another user on another related question--

"Caution: as noted in the links below, in actual practice, the distinction between E2 airspace and E3/E4 ("extension") airspace is often ignored by ATC..."
In the Center environment, we make no distinction between the surface area and the extensions when dealing with SVFR. The reason is simple. I can't clear a SVFR and an IFR in that airspace at the same time (or two SVFR aircraft), so those extensions should be empty if I'm allowing SVFR. Conversely, I'll not allow a SFVR operation (remember, the pilot has to request it), if I have an IFR aircraft cleared in that surface area.
In the case of Class E that's adjacent to Class C or D airspace, the pilot should be talking to ATC, anyway.
Keep in mind, though, if you're just buzzing along VFR and you see that there's a surface area ahead of you, there's nothing wrong with calling Center and asking if there's known traffic there, or even requesting flight following (cheap insurance!) through the area.

There's no reason to delete it. It seems there's a lot of confusion over Class E among pilots, and even within the FAA (don't even get me started on Class G), so the question is certainly relevant.

Revisiting this topic a few days later -- recognizing that SVFR traffic could not be allowed in any of the "surface area" (including the "extension") while any IFR traffic was also cleared to be there, and vice versa, doesn't automatically imply that the rules should be construed to allow SVFR in the "extensions" at all.  And naturally, an aircraft forced to choose between observing standard VFR rules in the "extensions", and keeping clear of the extensions, ought not be be having any effect on a controller's handling of IFR traffic either way.  Except for the fact that prohibiting (ctd)

(ctd) Except for the fact that prohibiting SVFR in the extensions could slightly speed up IFR traffic flow in some cases, though IFR traffic is always given priority anyway when deciding whether to accept/decline a SVFR requests, as I understand it.  Still, an informative answer, thanks.

atc_ceedee -- you are apparently not currently active on ASE, but if you return-- I would love to see this answer copied in entirety to https://aviation.stackexchange.com/q/64205/34686
, or possibly to https://aviation.stackexchange.com/q/48106/34686 .  It fits either of those-- especially the first-- perfectly.  And while it's considered bad form to delete answered questions on ASE, in this particular case I would delete this question after you made that cross-posting.  (Maybe you'd want to delete your answer here after cross-posting.)

(ctd)  I really feel that this question is just an "umbrella" question that is redudant with those, and some others, such as the ultralight question, and I regret having posted it in the first place.

As noted in several answers to this related ASE question, surface-level Class E airspace that actually surrounds the airport for which it is designated-- the airport whose airspace it is intended to protect-- is designated as E2 airspace.  Surface-level Class E "extensions" that protect the instrument approaches into other adjoining Class D (or surface-level Class E) airspaces are designated as E4 airspace.  E3 airspace is the same as E4 airspace, except that the
extension" is adjoined to Class C airspace rather then Class D or Class E "airspace.  E3a airspace the same as E4 airspace, except that the "extension" is adjoined to Class B airspace.  All this is spelled out in the FAA's "Airspace Designations and Reporting Points" document, current issue FAA Order 7400.11E.
The truth is that the FAA is deeply divided as to whether phrases in the FARs like "surface area", "designated for an airport", and "surface area of controlled airspace designated for an airport" should or should not be construed to include surface-level Class E "extensions", i.e. E3/E3a/E4 airspaces.1  Ambiguity around this issue has existed ever since the 1993 "alphabet" airspace re-designation.2  There's some consideration of a future rule-making effort to address this issue.3  It's possible that the language in AIM 3-2-6, as well as in the legend of the Chart Supplements, that reads "Surface area arrival extensions become part of the surface area and are in effect during the same times as the surface area" will be changed in the future to avoid implying that all regulations that apply to the core "surface area" should automatically be construed to apply to the surface-level Class E "extensions" as well.4
For a list of all the aviation activities that are potentially affected by whether or not phrases like "surface area", "designated for an airport", and "surface area of controlled airspace designated for an airport" are construed to include surface-level Class E "extensions", see the related ASE question What indication has the FAA given that phrases like "surface area of Class E airspace designated for an airport" do or don't include E4 "extensions"?.  Among other things, these activities include-- receiving a clearance for Special VFR flight, flying under a ceiling lower than 1000' AGL (without a Special VFR clearance), flying ultralight aircraft, flying unmanned aircraft (model airplanes, "drones", etc), flying unmanned free balloons, and performing aerobatics.
If phrases like phrases like "surface area", "designated for an airport", and "surface area of controlled airspace designated for an airport" are construed to include the surface-level Class E "extensions", then these activities would be prohibited (or in some cases, prohibited without "prior authorization") in the surface-level Class E "extensions".
On the other hand, if phrases like phrases like "surface area", "designated for an airport", and "surface area of controlled airspace designated for an airport" are construed not to include the surface-level Class E "extensions", then these activities would not be prohibited in the surface-level Class E "extensions".
Depending on the exact parsing of the meaning of the words, some of these phrases might be deemed to include the surface-level Class E "extensions" and others might be deemed not to, in which case some of the activities listed above would be allowed in the "extensions" and others would not.  It's a bit complicated.  Some of the regulations around Special VFR, in particular, do not actually include the phrase "surface area".
To learn more about the rationale behind construing these various phrases to include, or exclude, the surface-level Class E "extensions" (E3/E3/E4 airspaces), see this related ASE question.
Many examples can be found where the FAA is using the phrase "surface area" in a context that is clearly meant to exclude the surface-level Class E "extensions" (E3/E3a/E4 airspaces).  The above link explores whether or not that is the most correct understanding of the phrase in terms of interpreting the meaning of various FARs.  On the other hand, air traffic controllers often use the phrase "surface area" to mean the entire column of airspace that extends up from the surface in any given location, including any surface-level Class E "extensions" that may be present.  There are many examples in various FAA Orders where the word "surface area" is used in a way such that it is not clear which of these two usages is intended.
When thinking about the possible impact of the surface-level Class E "extensions" on various aviation activities, keep in mind that a) Class E airspace has no defined upper limit, except for where it superseded by some overlying higher class of airspace, and b) all of the relevant regulations are written in language that includes phrases like "within the lateral boundaries" of the surface-level Class E airspace in question (which may or include the "extensions", depending on the interpretation we are following), which means that the column of airspace addressed by these regulations has no defined upper limit whatsoever.  So construing various regulations to include the "extensions" puts rather large chunks of airspace off-limits to certain aviation activities-- e.g., flying an ultralight.
How to tell E2 airspace from E3/E4 ("extension") airspace on a sectional chart?
Here is an example of E4 ("extension") airspace-- look specifically at the airspace within the dashed magenta line that does NOT surround the airport whose approaches are being protected.  That is the E4 ("extension") airspace.  The airspace within the dashed magenta or dashed blue line that DOES surround the airport is D airspace (and in this case, reverts to E2 airspace when the tower is closed):
KMFR
On the other hand, none of the airspace enclosed by the dashed magenta line here is E4 ("extension") airspace.  It is all E2 airspace.   There is no dashed magenta line that does NOT enclose the airport:
KONP, KSHR
E3 and E3a airspace is depicted like E4 airspace but the dashed magenta "extension" abuts Class C or Class B airspace,  respectively, which is depicted differently than the dashed blue or dashed magenta circles in the examples above.
Here is an example of E3 ("extension") airspace--the dashed magenta boundary extending toward the northeast:
KSGF
Unfortunately there are a few exceptions to this clear distinction between how E2 and E3/E3a/E4 ("extension") airspaces are usually depicted. The ambiguity arises in the case of un-towered airports that have surface-level Class E (E2) airspace.  In some cases, long projecting areas of this airspace far from the airport have been included in the E2 airspace description (example: KSHR). In other cases, long projecting areas of this airspace have been designated as E4 airspace (examples: SIT/PASI, BIH, SGU, TVL, and ACV).  Of the latter 5 examples, only TVL and ACV have been charted in a way such that the boundary between the E2 airspace and the E4 airspace is actually visible on the sectional chart. The other three are charted just like KSHR, with a single dashed magenta line enclosing all the surface-level Class E airspace.  This is explored in more detail, with screenshots, in the related ASE question What is the primary reason that the non-towered airports ACV, TVL, SGU, BIH, and SIT/PASI have E4 extensions to E2 airspace?.  Presumably the charting agency will eventually standardize on one of the two methods--and then in the future may need to change the convention, if the FAA definitively determines that there are indeed significant regulatory differences between surface-level Class E "extensions" (E3/E3a/E4 airspaces), and the core surface-level Class E "surface areas" (E2 airspaces) that actually surround the airports for which they are designated.
Footnotes:
1,2,3,4) Source-- comments made by high-level FAA staffers during April 2021 airspace charting meeting.
Related ASE questions and answers:
A: Does an SVFR clearance extend to Echo surface extensions?
A: Does an SVFR clearance extend to Echo surface extensions?
A: In the US, in actual practice, workload permitting, will ARTC facilities grant SVFR clearance for surface-level Class E “extensions” (E4 airspace)?
A: Does FAR 91.155c apply to class E surface extensions?
Q: What indication has the FAA given that phrases like "surface area of Class E airspace designated for an airport" do or don't include E4 "extensions"?
A: What indication has the FAA given that phrases like “surface area of Class E airspace designated for an airport” do or don't include E4 “extensions”?
Q: Which parts of class E airspace can an ultralight (part 103) fly in without prior ATC authorization?

Lovin' the dv's, as always...

You have a few duplicate named links to your other E2/E4 soliloquies.

@MichaelHall -- as for the list at the end-- in one case I felt both the question and the answer contained significant information.  As for the two links at the very top, one goes to someone else's answer.  Does that cover everything you were noticing, or am I missing something?  Yes some links embedded in the article may duplicate some of those, I wanted to give a consolidated list at the end.

@MichaelHall -- anyway that pretty much wraps the round of edits that reflects a significant change in my perspective over the last couple of years.  The main thing still in need of a significant update is the answer to https://aviation.stackexchange.com/questions/64246/what-are-the-historical-precedents-of-todays-e2-and-e4-airspace-us?noredirect=1&lq=1 , which is missing a lot of details I've since unearthed...

Your obvious passion and dedication to these minor distinctions is admirable, but I believe the body of your work on the topic is disproportional to the effect on a majority of us, and is in general beyond the scope of a Q&A site like this.  And frankly I am growing weary of the duplication and constant edits popping these to the top of the active questions.

@MIchaelHall -- I'll leave it alone for a while now-- still, I don't fully agree that the topic should be beyond the scope of this site.  We've seen some rather detailed answers on many topics (Peter Kampf comes to mind) -- anyway, whatever, got to go to something else now.

The sentence "To learn more about the rationale behind construing these various phrases to include, or exclude, the surface-level Class E "extensions" (E3/E3/E4 airspaces), see this related ASE question." could have been better phrased as  "To learn more about the rationale behind construing these various phrases to include, or exclude, the surface-level Class E "extensions" (E3/E3/E4 airspaces), see the link given above."  (To avoid repeating the same link twice in the body of the answer.)

Re "Presumably the charting agency will eventually standardize on one of the two methods" -- apparently that has now happened.  The depiction of the airspace at KACV has been modified to drop the dashed magenta line dividing the core E2 circle from the E4 "extension".  Meanwhile the airspace structure at KTVL has been changed to entirely drop the E4 extension.

As a result of these changes, there seem to be no remaining examples on current sectional charts that show the dividing line between a Class E "surface area" (E2 airspace) and a surface- level Class E "extension" (E4 airspace).  (Except of in cases where the E2 airspace sometimes switches to Class D or higher airspace due to a control tower being in operation.)

Future edit -- "So construing various regulations to include the "extensions" puts rather large chunks of airspace off-limits to certain aviation activities-- e.g., flying an ultralight, or performing aerobatics."


text:
In the modern aviation context, is the word "supercharger" generally assumed to mean a gear-driven system rather than an exhaust-driven system?
In the modern aviation context, is the word "supercharger" generally assumed to mean a gear-driven system rather than an exhaust-driven system?
At one time the word "supercharger" often was used to encompass both turbosuperchargers (aka turbochargers) which were exhaust-driven, and gear-driven superchargers.  But I have seen the word "supercharger" used to specifically mean a gear-driven system as distinct from an exhaust-driven system.  Would this usage be generally considered unambigous and good practice in the modern aviation context?  Or at least, very common practice in the modern aviation context?
(Include belt-driven along with gear-driven, if such a thing even exists in aviation engines.  The question is about exhaust-driven versus mechanically-driven devices, and how these two different sorts of devices map out against the various terminology in current aviation use.)
A supplemental question might be: "Has the word 'turbosupercharger' completely disappeared from modern aviation terminology?"

Having been in the "tuner" world for a long time, I've never heard of a supercharger being referred to as both a gear driven device and an exhaust driven one.

Sounds like you are well qualified to answer, perhaps. - Is "tuner" an automotive reference or an aeronautical one?

I'd agree with @RonBeyer. From an automotive perspective, a "turbocharger" is exhaust driven while a "supercharger" is gear/belt driven, and nary the twain shall meet. There are some variations of "twin-charger" (or similar name) which has a supercharger for off-the-line power and a turbocharger for once you're moving. The supercharger saps a lot of horsepower to make even more, while the turbocharger is nearly free power. And yes, "tuner" as in "automotive tuner".

@FreeMan Anecdote: The other day I watched an episode of The Grand Tour. They drove some extreme car with almost 1000 hp and said the supercharger "takes" 110 hp from the engine but "gives" 500 hp in return. :-)

Wikipedia on "supercharger" -- "Common usage restricts the term supercharger to mechanically driven units; when power is instead provided by a turbine powered by exhaust gas, a supercharger is known as a turbocharger or just a turbo - or in the past a turbosupercharger.[1]  "  -- however this reference is not specifically aimed at the aviation context where a ghost of the older terminology may or may not still linger--

Future project, future edit: find specific citations for "supercharger" being used to encompass both systems.  Will not be hard to find in aviation sources from the 20's, 30's, 40's.

@FreeMan Ok, I mixed up the numbers. It was a Corvette ZR1 with 755 hp. The supercharger takes 110 hp to run but returns 290 hp.

A modern top fuel dragster's supercharger can take upwards of 1000HP to drive it. But it returns significantly more. </OT musings>

Related question.  One answer uses the term "superturbocharger" in a way that I don't think is really an accepted usage.  (I've never seen this word before at all.)   https://aviation.stackexchange.com/questions/33407/in-high-altitude-piston-aircraft-what-type-of-forced-induction-boost-is-used/33409

If you want to have fun, look up "turboencabulator" and watch some of the videos.

This question is now also addressed here (completely forgot about this older question, even though it was asked by me, when I wrote the newer answer) -- https://aviation.stackexchange.com/a/100180/34686

"Turbosupercharger" was General Electric's official term for their system, probably the first mass produced turbocharging system and was used on a range of US fighters and bombers (the system was very sensitive to back pressure in the turbine outlet which could promote stalling, and so they either had the turbine exposed like on the P-38, or if there was an exhaust duct it was very very short).
Anything that compresses the intake charge is a supercharger. Prior to the GE system, they were all mechanically driven and the mechanical drive naturally had horsepower losses associated with that type of drive.  GE added the word turbo to differentiate between the common gear driven or direct driven supercharger and their new and novel system that eliminated most of the energy losses from compressing air.
Move forward into the post war era and the adoption of systems to cars and light aircraft and people get annoyed having to say this pain in the butt 6 syllable word and start to cut out the "super" part, because it doesn't really detract from the meaning, and there you are with "turbocharger" for both cars and airplanes.
Meanwhile, "supercharger" stays as it always was and remains associated with mechanical systems, because the terms, although incomplete technically, don't contradict each other on common usage they continue.

Nice answer but I would like to know how early the GE system was introduced, would be a nice addition to the answer.  Was it really the earliest turbocharger?  I'm sure I've seen photos of turbochargers on aircraft from the '20's.  OK you didn't say it was the earliest turbocharger; isn't it possible that "turbosupercharger" was already used for for very early non-GE systems?  If so would be worth noting in answer.

As a mass produced production system, yes.   Late 30s.  I stumbled onto a link to a GE pamphlet and added it at the top.

Got it; see slight tweak to comment.

Not aware the details of earlier turbocharger systems, but I refer to "mass production" as something that had become common enough to filter into the public consciousness, as opposed to low volume or experimental systems developed prior.

The GE turbosupercharger was developed in 1917 and was the product that moved GE into aviation. From the GE Aviation Blog.

And there ya go.  But they weren't in what you could call mass production until the Army contracts in the 30s.

Piston engine model numbers still use the "TS" prefix for TurboSuperchargers rather than just "T".

The GE Aviation Blog link doesn't really make it clear that the 1917 / 1919 product was an exhaust-driven device, or that the word turbosupercharger was really applied at that time, and even seems to hint (possibly inaccurately) that "turbo" might have originally referred to the compressor wheel rather than a turbine in the exhaust stream.   Still, it's worth a read.

Don't forget turbonormalizer - a turbocharger that only boosts to sealevel pressure.  Seen on small planes.
https://taturbo.com/tnvtc.html
https://taturbo.com/177features.html

And then there's always turbocompound...

Never seen on small planes!


text:
How common are gear-driven or belt-driven superchargers in modern aircraft?
How common are gear-driven superchargers in modern piston-engine aircraft, either alone or in combination with exhaust-driven turbochargers? What are some examples of modern aircraft that use them? Is it a technology that essentially went extinct in the aviation context with the last of the piston-engined fighters, bombers, and large airliners? Such that turbocharging alone (or other variants such as turbonormalizing) is the preferred technology for piston-engine aircraft now?  (Besides the old standby of normally aspirated engines of course.)
How about belt-driven superchargers-- do any aircraft have them?  If so, which ones?
Feel free to consider homebuilt aircraft, experimental aircraft, lightsport aircraft, and automotive conversion engines in your answer.
Edit: in light of a recent comment, I'll add that I'm asking about devices that are used at least in part to increase thrust and power by feeding pressurized air to the engine, rather than only to pressurize the cabin.

Not really an answer to your question, but most pressurized pistons use a gear or belt driven supercharger not for increased power but for providing pressurization.
It should be noted that most of these aircraft also have a ground normalized turbo-charger for power at altitude as well.

I'd say it's at least a partial answer, thanks!  I didn't even consider that possibility though its kind of obvious in hindsight.

Radial engines like the P&W R-985 contain a gear-driven impeller disc that spins at greater-than-crankshaft speed and centrifugally stirs the fuel/air mixture around in the intake manifold so that each cylinder gets the same mixture as all the others. However, by increasing the gear ratio it is possible to get a supercharging effect in addition to the mixture distribution effect. at least one Beech Staggerwing with the R-985 engine had the original fan ratio increased to 22:1 to improve hot & high takeoff performance. Don't know how common this mod was.

@nielsnielsen that's worthy of an answer

I would say that supercharging is much more simple solution than turbocharging. It has some use in cars as there is no turbo lag and that is not actual in planes. Turbocharging recovers otherwise wasted exhaust gas energy and supercharging just uses engine increasing consumption. Turbocharging technology has advanced a lot so it doesn't make sense to use supercharging'

Over the years attending and serving tech functions at the Reno Air Races, there has been at least one Sport Class entrant with a belt driven centrifugal supercharger. One that really stood out was a Sport Class entrant with a chainsaw motor driven centrifugal supercharger mounted in the "copilot" position. It blew through an ice chest intercooler. Never did very well though.

Lycoming offered mechanical superchargers in some of their large 6 and 8 cylinder opposed engines like the GSO-480 but such engines have been out of production a long time.
I would say the only mechanical superchargers to be found on any engines manufactured today would be found on Russian or similar Eastern European radial engines like the M14P.
I'd be pretty shocked to hear of a homebuilder incorporating a mechanical supercharger, but maybe somebody will find an example. In any case, if you're going to do it, so much easier to do it with a turbo.  The thing that makes turbocharging difficult to work seamlessly in cars, the power lag issue, isn't a problem with aircraft, so a turbo is a no-brainer that can be done by the homebuilder on just about any engine if they really want it.  To incorporate a mechanical drive system on an engine not designed for it would be quite a daunting task.

Radial engines like the P&W R-985 contain a geared impeller disc that centrifugally slings the fuel/air mixture around in the manifold from the carb out to the intake runners for each cylinder. This disc spins at greater-than-crankshaft speed and is intended to stir the mixture sufficiently well so that each cylinder is feeding on the same mixture as all the others. However, by changing the gear ratio it is possible to get a supercharging effect in addition to the mixture distribution effect. This was done in at least one instance in a Beech Staggerwing with the R-985 engine where the original fan ratio was changed up to 22:1 to improve hot & high takeoff performance. I do not know how common this practice was.

The Reno Air Races, Unlimited Class P51s have stepped-up superchargers. Stock max manifold pressure is around 75 inches. Unlimiteds go as high as 150 inches or possibly higher these days. Lots of ADI fluid injection and liquid manganese in the fuel, though.


text:
Does the FAA construe FAR 91.225 to prohibit aircraft w/o electrical systems w/o ADS-B-out from flying above 10,000' MSL unless below 2500' AGL?
For airspace within the 48 contiguous states and the District of Columbia:

For aircraft originally certificated without engine-driven electrical systems (and not subsequently certified with such a system installed), and lacking ADS-B-out, does the FAA construe FAR 91.225 as imposing a general prohibition on flight in Class E airspace above 10,000' MSL (excluding airspace below 2500' AGL)??

For aircraft originally certificated without engine-driven electrical systems (and not subsequently certified with such a system installed), and lacking ADS-B-out, does the FAA construe FAR 91.225 to prohibit flight above 10,000' MSL in Class E airspace that lies directly above the ceiling of Class B or Class C airspace?

For example, does the FAA construe FAR 91.225 to prohibit a glider without ADS-B-out from exceeding 10,000' MSL in Class E airspace, unless it is not above 2500' AGL?
If possible, please support your answer by referencing specific FAA materials, including information/educational materials and/or official interpretations from the Office of the Chief Counsel.
The current question is not about the significance of the phrase "without electrical systems" rather than "without engine-driven electrical systems" in FAR 91.225.  This letter of interpretation from the FAA Office of the Chief Counsel clarifies that the references to aircraft "without electrical systems" in FAR 91.225 should be understood to instead read aircraft "without engine-driven electrical systems", and that the omission of the phrase "engine-driven" was in fact simply a mistake.  (Update: this issue has now been corrected.)
The original motivation for this question was a (pre-2020) conversation at a glider club where some pilots stated that their understanding was that once FAR 91.225 went into effect, gliders without ADS-B-out would not be able to legally exceed 10,000' MSL, unless below 2500' AGL.
Some context on why FAR 91.255 is arguably ambiguous in relation to the specific questions asked here may be found in this related ASE answer: FAR 91.215 (b)(3)(ii)-- transponders- significance of "Below the altitude of the ceiling of a Class B or C airspace area... or below 10,000' MSL..."

Link to letter of interpretation needs updating -- the current link is https://www.faa.gov/about/office_org/headquarters_offices/agc/practice_areas/regulations/interpretations/Data/interps/2017/Schober_2017_Legal_Interpretation.pdf

Opening paragraphs would be more clear if said "...does the FAA construe FAR 91.225, and specifically d(3) in combination with e(2),  as imposing (/to prohibit).  Likewise final sentence-- "A full description of why FAR 91.255 (and specifically d(3) in combination with e(2) is ambiguous and might be interpreted as per either of the opening paragraphs above may be found in this related ASE answer... "

The content in this FAA link indicates that the answer to both of our questions is "no":

Under the rule, ADS-B Out performance will be required to operate in:

Class A, B, and C airspace.
Class E airspace within the 48 contiguous states and the District of Columbia at and above 10,000 feet MSL, excluding the airspace at
and below 2,500 feet above the surface.
Class E airspace at and above 3,000 feet MSL over the Gulf of Mexico from the coastline of the United States out to 12 nautical
miles.
Around those airports identified in 14 CFR part 91, Appendix D.

The ADS-B Out rule does not apply in the airspace defined in items 2
and 4 above for any aircraft not originally certificated with an
electrical system or that has not subsequently been certified with
such a system installed, including balloons and gliders. For
additional requirements for using the exception for item 4, please
refer to CFR 91.225 section (d) for the requirements.

(italicization added)
Note however that this statement suffers from at least one obvious omission.  It omits the airspace described in 91.225(d)(3)-- namely the airspace directly above a Class B or Class C ceiling, upward to 10,000'.  With that in mind, it seems unwise to rely on this statement in relation to the second of the two questions above.
(As of Feb 24 2020, the quoted web page had last been updated on August 22, 2019.  As of February 12 2023, the link is inoperative.)
Also, a 2019 Legal Interpretation from the Office of the Chief Counsel contains the following statements (second-to-last paragraph of page 2), which again indicate that the answer to both of our questions is "no":

Similarly, the FAA did not intend the operating condition in § 91.225(
e)(2) to prohibit or limit § 91.225(e) aircraft from operating in the
airspace identified in§ 91.225(d)(4). Rather, § 91.225(e)(2) applies
solely to the airspace addressed in § 91.225(d)(2).

and

Therefore,§ 91.225(e)(2) also does not affect operations in the
airspace specified in§ 91.225(d)(4).

A close look at the actual logic used to justify these statements suggests that it is rather defective.  It seems that the FAA is issuing interpretations based on the effect they intended the rules to have, rather than the actual language of the regulations.  Which can arguably be described as "just making it up as you go along".  It would be have been better to make the effort to write clear language that actually delivered the intended meaning, rather than creating a linguistic and logical "train wreck" by importing language whose meaning was already unclear in an older regulation (FAR 91.215), into a new regulation (FAR 91.225) where its meaning and effect would be even more unclear, by virtue of the larger span of altitude affected by the relevant portions of the new regulation.
But this interpretation is beneficial to pilots of sailplanes, balloons, antique aircraft, etc.  When FAR 91.225 was first introduced via a Notice of Proposed Rule-Making, it's surprising that these pilots, and especially their national organizations, didn't take note of the potential ramifications of the ambiguities in the regulations (and specifically in the language of 91.255(e)(2)) and intervene to bring about clearer language.  After all, any given legal interpretation by the FAA can always be superseded by another one, so it's better to be able to rely on the actual language of the regulations.

The link needs updating -- if the quoted content still exists on line at all.

Related-- https://aviation.stackexchange.com/questions/65930/far-91-215-b3ii-transponders-significance-of-below-the-altitude-of-the/65934#65934 -- especially the new content after the dashed line--

This AOPA article https://www.aopa.org/news-and-media/all-news/2017/january/19/ads-b-requirement-clarified-for-nonelectrical-aircraft implies that the FAA construes 91.255 to prohibit aircraft (even those lacking engine-driven electrical systems) from operating anywhere above the ceilings of Class B and Class C airspace.  This would be a significant change from how they interpret 91.215.

RE "by importing language whose meaning was already unclear in an older regulation (FAR 91.215),"-- this would be a good place to link to https://aviation.stackexchange.com/q/65930/34686 (see especially "Question 4"), and https://aviation.stackexchange.com/a/74860/34686.


text:
At what altitude, if any, may an ultralight overfly the Gallup airport (KGUP) with no prior authorization without violating FAR 103.17?
At what altitude, if any, may an ultralight overfly the Gallup, New Mexico airport (KGUP) with no prior authorization without violating FAR 103.17?
This is a question about the meaning of

"within the lateral boundaries of the surface area."

Resources--
FAR 103.17 --

"No person may operate an ultralight vehicle within Class A, Class B, Class C, or Class D airspace or within the lateral boundaries of the surface area of Class E airspace designated for an airport unless that person has prior authorization from the ATC facility having jurisdiction over that airspace."

Sectional chart depicting KGUP
Description of the E2 airspace at KGUP-- from page E-116 of the FAA's "Airspace Designations and Reporting Points" document FAA Order 7400.11D--

"ASW NM E2 Gallup, NM
  Gallup Municipal Airport, NM
   (lat. 35°30'41"N., long. 108°47'15"W.)
  Gallup VORTAC
   (lat. 35°28'34"N., long. 108°52'21"W.)
Within a 4.1-mile radius of Gallup Municipal Airport and within 1.3 miles each side of the 242° radial of the Gallup VORTAC extending from the 4.1-mile radius to 4.9 miles southwest of the airport."

Note that no limitation is given as to the time of day that the E2 airspace is in effect, and therefore it is in effect 24/7.  No specific altitude limit is stated in this section, though on page E-1 we read--

General.

Generally, if the airspace is not Class A, Class B, Class C, or Class D, and it is controlled airspace, it is Class E airspace. Class E airspace extends upward from either the surface or a designated altitude to the overlying or adjacent controlled airspace. When designated as a surface area, the airspace will be configured to contain all instrument procedures. Also in this class are Federal airways, airspace beginning at either 700 or 1,200 feet above ground level used to transition to/from the terminal or enroute environment, and enroute domestic and offshore airspace areas designated below 18,000 feet MSL. Class E airspace does not include the airspace 18,000 feet MSL or above.

I guess this question was also asked in https://aviation.stackexchange.com/questions/35297/which-parts-of-class-e-airspace-can-an-ultralight-part-103-fly-in-without-prio but only as a single part (part 4) of a complicated multi-part question that was really more foccused on the horizontal extent of where an ultralight may fly.  I would suggest that the vertical aspect merits being addressed in a specific question on its own.

This question is not the same as https://aviation.stackexchange.com/questions/65366/may-an-ultralight-vehicle-pass-directly-above-kege-at-9200-msl-at-1600z-with-no , because KEGE is an oddball case, involving a possibly defective airspace description, where it is unclear whether or not E2 airspace is supposed to be in effect directly over KEGE at the same times of day that the Class D airspace is in effect.

Highly related-- note the specific reference to FAR 103.17 -- https://aviation.stackexchange.com/questions/74979/what-does-the-faa-mean-by-within-the-lateral-boundaries-of

An interesting point is that in some of the rule-making documents leading up to the September 1993 "alphabet" airspace re-designation, the FAA proposed allowing ultralights to operate in (or within the lateral boundaries of) the surface-level Class E airspace designated for airports so long as these operations were conducted above a certain altitude which I recall was something like 4000 or 5000' AGL-- which was also the standard ceiling that was being proposed at the time for Class D airspace-- the question or answer might benefit from a more thorough note on this fact.

This is really a better question that gets at the same issues -- https://aviation.stackexchange.com/questions/74979/in-reference-to-airspace-what-does-the-faa-mean-by-within-the-lateral-boundari -- this other question shouldn't be deleted as a duplicate because it is broader in scope, while the present question can't be deleted as a duplicate because it has received several answers, one of which has been upvoted.

You can not fly an ultralight there without prior authorization if I am reading 103.17 correctly. The way that I am reading this, it seems that you may not be in controlled airspace around an airport without prior authorization, period. And, above  18000 is a no-go as well.
The highest concentration of aircraft traffic is at airports, Navaids like VORs, and on airways. You want to steer clear of those unless you are in clear and direct communication with those in charge of the airspace. Gallup has all three.
As far as Class E airspace, the way that 103.17 reads, It makes it sound like you are not allowed to fly in any Class E airspace over an airport without prior authorization. Admittedly, it’s splitting hairs. Everywhere else in 14 CFR, the description of Surface Class E has slightly different verbiage.

103.17 Operations in certain airspace.
  No person may operate an ultralight vehicle within Class A, Class B, Class C, or Class D airspace or within the lateral boundaries of the surface area of Class E airspace designated for an airport unless that person has prior authorization from the ATC facility having jurisdiction over that airspace.
137.43 Operations in controlled airspace designated for an airport.
  (b) No person may operate an aircraft in weather conditions below VFR minimums within the lateral boundaries of a Class E airspace area that extends upward from the surface unless authorization for that operation has been obtained from the ATC facility having jurisdiction over that area.
3–2–6 Class E Airspace
  1. Surface area designated for an airport where a control tower is not in operation. Class E surface areas extend upward from the surface to a designated altitude, or to the adjacent or overlying controlled airspace. The airspace will be configured to contain all instrument procedures.

You might want to edit to say "in controlled airspace around an airport with a Class E surface area..."   If we were talking about an airport like Flagstaff http://vfrmap.com/?type=vfrc&lat=35.140&lon=-111.669&zoom=10&api_key=763xxE1MJHyhr48DlAP2qQ, you would be fine to be in the Class E that exists above the Class D, above 9500' feet, it seems to me.

Actually that same verbiage is used in several other FARs.  I'll list them later in a comment or answer.

Whether or not it's legit or not for an ultralight (which may or may not be ADS-B Out equipped) to be overflying that airspace without talking to ATC, if you take into account that IFR approaches start from 9500 feet and could be as low as 7500 feet with a missed approach starting with climb to 9500 feet in the airport vicinity, and some planes can do that pretty quick, I'd say you'd want to be at least 10500 feet westbound and 11500 feet eastbound for separation purposes.  IFR traffic will be given advisories about you, if you're not talking to ATC then you could be in for a surprise.
IFR plates for KGUP can be found here  https://www.airnav.com/airport/KGUP

Ultralights don't need ADS-B-out or transponders.  It is not legal to put ADS-B-out on an unregistered aircraft.

I see suggestions to put one of these in Ultralights with a blank N-Number field.  I would like to be aware of all traffic around me when I am flying.  https://uavionix.com/products/ping2020/

Consider that you also might meet a sailplane legally flying with no transponder.  Mark one eyeballs see-and-be-seen is the rule for all traffic, even IFR traffic, outside of IMC conditions, in most airspace below 18000 MSL.

Consider also that Part 91, Section 1(e), states that ultralight vehicles are exempt from Part 91 in its entirety.


text:
Does this web page really correctly depict the angle that is called "incidence" in the French language in the aviation context?
Does this web page really correctly depict the most common usage of the term "incidence" in the French language in the aviation context, in the context of speaking of an entire aircraft and not just an isolated part such as a wing section in a wind tunnel?  Is the label "incidence" really attached to the correct angle?
I am referring specifically to the second airplane diagram, i.e. the first diagram that shows an airliner.   Note that the text above the diagram uses the phrase "en croisière" which is a reference "cruising", presumably horizontal, flight.  The line x-x' appears to represent the longitudinal axis of the aircraft, so it appears that the angle labeled "incidence" represents the angle between the flight path/ relative wind and the longitudinal axis of the fuselage, not the angle between the flight path/ relative wind and the chord line of the wing, which would clearly be a larger angle.
In fact the text above the diagram explicitly states "L'incidence est définie par rapport à l'axe de l'aéronef et non de la voilure.", which translates to something like "The incidence is defined relative to the axis of the aircraft and not of the wing."
Shouldn't the angle labeled "incidence" be the angle between the flight path/ relative wind and the chord line of the wing rather than the angle between the flight path/ relative wind and the fuselage?
Or is it just a matter of arbitrary convention, meaning that either usage would be equally appropriate?
(One way to concisely answer this question might be "The correct usage of 'angle d'incidence' in the French aviation context is exactly identical to the English-language usage of 'angle of attack' (or replace with other appropriate angle as needed) as noted in this ASE answer (give link)."  Not all ASE answers have given the same perspective on the most correct usage of this term.)
Note that the angle labeled "angle de calage" is the angle that is called "incidence" in American aviation usage and some or most (but not all) British aviation usage-- the angle between the chord line of the wing and the longitudinal axis of the fuselage.  This question is not about whether or not the diagram uses "angle de calage" correctly in the context of French aviation terminology-- it clearly does.
Bonus question-- in the French aviation context, is the term "angle d'attaque" used to mean something different than "angle d'incidence"?

A Belgian instructor (french-speaking) told me "angle d'incidence" must be translated as "angle of attack" and "angle d'attaque" should not be used in french because it is confusing.

@ManuH -- that seems as worthy of being an answer as anything else that is likely to be submitted re this question.

For me it is just an anecdote as I don't have written references to support the answer, and thus it does not meet quality standard required to be an answer.

@ManuH -- ok, thanks for the comment anyway, it is useful.

Yeah it's right if we consider that the relative wind is parallel to the ground.
In French, the "angle d'incidence" is the angle between the chord line and the relative wind, contrary to the US and UK which it's the angle between the chord line and the longitudinal axis.(fr="angle de calage")

In french: In fluid mechanics, "l'angle d'incidence" is the angle formed by the chord of a profile and the relative wind speed vector. In English l'angle d'incidence" is called angle of attack (AOA).
  Attention, angle of incidence in English corresponds in French to the "angle de calage", the angle formed by the reference chord of a wing and the longitudinal axis of the aircraft.
  L'incidence (fr) notes : α

"Croisière" is cruise flight .the picture of the website is not clear because it confusing chord line and longitudinal axis(perhaps to simplify)... other important notion: RELATIVE WIND is the relative movement of air relative to the plane; it is ALWAYS PARALLEL AND SENSE OPPOSITE to the TRAJECTORY OF THE AIRPLANE(path)
Source: (the second link is french because the same page is different in French and in English)
https://fr.m.wikipedia.org/wiki/Incidence_(a%C3%A9rodynamique)
https://www.lavionnaire.fr/AerodynCPFoyer.php

I know we've talked about this before and thanks for the clarification again about how incidence is used in French but I think your answer should say the first airliner diagram is wrong because it specifically labels the incidence angle as something different than what you are saying here.  Only in the second airliner diagram, not the first, are the chord line of the wing and the longitudinal axis of the fuselage shown as being the same thing for simplicity.

@quiet flyer (For me )to sum up:the picture is not clear...but this picture show more the "angle de calage" than "angle d'incidence" .the site show the "angle d'incidence" on first picture.so if the "incidence" in the picture is not correct,less important than the "angle de calage" which is correct

If you consider that it's not correct contact them and see with they.